Monitoring one or more solutes in a biological system using optical techniques

ABSTRACT

This invention is a scheme for monitoring a solute in a biological system comprising the steps of delivering light into a biological system ( 12 ) containing a solute, the light having a wavelength selected to be in a range wherein the solute is substantially non-absorbing; detecting at least first and second portions of the delivered light, the first portion having traveled through the biological system along one or more paths characterized by a first average path length, and the second portion having traveled through the biological system along one or more paths characterized by a second average path length that is greater than the first average path length; and comparing the first and second portions of the delivered light to monitor concentration of the solute in the biological system. Also described are schemes for monitoring low molecular weight polyhydroxy solutes, generally sugars (mannitol, fructose, sucrose, glucose, sorbitol), alcohols (methanol, ethanol, propanediol), and electrolytes (sodium, potassium, magnesium, calcium, and chloride ions).

This application is a continuation of U.S. application Ser. No.10/299,598, filed on Nov. 19, 2002, now U.S. Pat. No. 6,957,094; whichis a continuation of U.S. application Ser. No. 08/849,203, filed on Jun.2, 1997, now U.S. Pat. No. 6,493,565; which claims priority under 35U.S.C. §371 from PCT application PCT/US95/15666, filed on Dec. 4, 1995;which is a continuation-in-part of U.S. application Ser. No. 08/349,839,filed on Dec. 2, 1994, now U.S. Pat. No. 5,782,755.

BACKGROUND

This invention relates to in vivo monitoring one or more solutes in abiological system using optical techniques.

Monitoring the concentration of a solute (e.g., low molecular weightcarbohydrate or polyhydroxy compounds such as sugars (mannitol,sorbitol, fructose, sucrose, or glucose), alcohols (methanol, ethanol,or propanediol), and electrolytes (sodium, potassium, magnesium,calcium, or chloride ions)) in a biological system has importantapplications in the medical field. For example, it is important fordiabetics, who have gone off insulin, to monitor their glucose level sothat can remedy any serious deviation in the level before harm occurs.

Near infra-red radiation (NIR) has been used to study non-invasively theoxygen metabolism in tissue (for example, the brain, finger, or earlobe). Using visible, NIR and infra-red (IR) radiation for medicalimaging could bring several advantages. In the NIR or IR range thecontrast factor between a tumor and a tissue is much larger than in theX-ray range. In addition, the visible to IR radiation is preferred overthe X-ray radiation since it is non-ionizing; thus, it potentiallycauses fewer side effects. However, with lower energy radiation, such asvisible or infra-red radiation, the radiation is strongly scattered andabsorbed in biological tissue, and the migration path cannot beapproximated by a straight line, making inapplicable certain aspects ofcross-sectional imaging techniques.

SUMMARY

In a general aspect, the invention features a scheme for monitoring one(or more) solute in a biological system comprising the steps of:delivering light into a biological system containing one (or more)solute, the light having a wavelength selected to be in a range whereinthe one (or more) solute is substantially non-absorbing; detecting atleast first and second portions of the delivered light, the firstportion having traveled through the biological system along one or morepaths characterized by a first average path length, and the secondportion having traveled through the biological system along one or morepaths characterized by a second average path length that is greater thanthe first average path length; and comparing the first and secondportions of the delivered light to monitor concentration of the one (ormore) solute in the biological system.

Embodiments of the invention may include one or more of the followingfeatures. Comparing the first and second portions of the delivered lightpreferably comprises obtaining a characterization of the biologicalsystem based on a linear model relating an optical characteristic of thebiological system and the first and second average path lengths. Thecharacterization that is obtained may be the slope and/or the interceptof a line determined by fitting to the linear model measuredcharacteristics of the first and second portions of light and distancesrepresentative of the first and second path lengths. Obtaining acharacterization may comprise obtaining measures of first and secondoptical densities of the biological system based on the first and secondportions of detected light and fitting the measures of optical densitiesto the generally linear model. Comparing the first and second portionsof the delivered light may comprise determining a measure of theconcentration of one or more of the solutes based on a comparison of thecharacterization of the biological system against a predetermined scale.

The monitoring scheme may further comprise determining a measure of aconcentration of one or more of the solutes in the biological systembased on a predetermined concentration scale. Detecting the first andsecond portions of the delivered light preferably comprises measuringfirst and second intensities (I₁, I₂) corresponding to the intensitiesof the first and second portions of light, respectively.

The monitoring scheme may further comprise determining changes, overtime, in the first and second intensities (I₁, I₂) relative to first andsecond reference intensities (I_(1,ref), I_(2,ref)). Determiningrelative changes in the first and second intensities may furthercomprise respectively determining first and second optical densities(OD₁, OD₂):${OD}_{1} = {\log\quad\left( \frac{I_{1}}{I_{1,{ref}}} \right)}$${OD}_{2} = {\log\quad{\left( \frac{I_{2}}{I_{2,{ref}}} \right).}}$Comparing the first and second portions of the delivered light maycomprise using a linear model relating the first and second opticaldensities to distances (ρ₁, ρ₂) representative of the first and secondaverage path lengths to obtain a characterization of the biologicalsystem representative of the concentration of one or more of the solutesin the biological system. The characterization that is obtained is aslope (m) may be determined by$m = {\frac{{OD}_{2} - {OD}_{1}}{\rho_{2} - \rho_{1}}.}$The characterization that is obtained may be an intercept (b) determinedby$b = {\frac{{{OD}_{1} \cdot \rho_{2}} - {{OD}_{2} \cdot \rho_{1}}}{\rho_{2} - \rho_{1}}.}$

The monitoring scheme may further comprise detecting a third portion ofthe delivered light, the third portion having traveled through thebiological system along one or more paths characterized by a thirdaverage path length that is greater than the first and second averagepath lengths.

In another aspect, the invention features a system for monitoring one ormore solutes in a biological system comprising: at least two sources oflight having a wavelength selected to be in a range wherein at least oneof the one or more solutes is substantially non-absorbing, a detectorpositioned at different distances with respect to the at least twodetectors to detect at least first and second portions of the deliveredlight, the first portion having traveled through the biological systemalong one or more paths characterized by a first average path length,and the second portion having traveled through the biological systemalong one or more paths characterized by a second average path lengththat is greater than the first average path length, and a comparatoradapted to compare the first and second portions of the delivered lightto monitor a concentration of one or more of the solutes in thebiological system.

In one embodiment of the invention, two or more continuous light sourcesare used and light reflectance at separated input-output distances aremeasured. Approximation of the exact solution for the spatially resolvedreflectance at separations larger than 2.5 cm provides a linearrelationship between the separation and absorbance variation withrespect to a reference sample. Slope and intercept of this straight lineare functions of the absorption and scattering coefficients (μ_(a) andμ_(s)′) of the measured sample. Using this technique, high measurementsensitivities for solute concentrations in a biological system can beachieved. For example, absorbency changes of approximately 0.2 milli ODare obtained for a 1 millimolar concentration change of the solute andper 1% change of the intralipid concentration.

Solutes contained in a biological system respond to migratingnear-infrared and infrared light by acting primarily to scatter theapplied light. The signal intensity of such migrating light is affectedto a greater extent the longer the average path length migrated by thedetected light. This enables us to obtain a linear relationship betweenan optical parameter of the biological system and at least two distancesrepresentative of average path lengths traveled by the detected lightthrough the biological system (e.g., at least two different sourcedetector spacing).

Solutes include low molecular weight carbohydrates such as sucrose,glucose, mannitol, sorbitol, inositol, maltose, lactose, galactose, andglucuronic acid; and hydroxy-functionalized compounds such as alcohols(methanol, ethanol), phenols, catechols, and flavanoids (e.g.,flavanones, flavones); and metabolites and metabolic precursors thereof.Solutes also include neurotransmitters such as amino acids(γ-aminobutyric acid, glycine, glutamate), choline, acetylcholine,norepinephrine, epinephrine, dopamine, serotonin, and histamines; andelectrolytes (sodium, potassium, magnesium, calcium) and other solubleions of the IA, IIA, and VIIB groups of the periodic table. Solutes arepresent in the interstitial spaces between cells, present within cells,or present in the blood (e.g., soluble in serum), or a combinationthereof. They may be released from or taken up by cells as intra- orinter-cellular messengers, as metabolites (or byproducts), or asmetabolic precursors or nutrients.

Solutes may be labelled with one or more radioisotopes of H, C, O, S, orP (e.g., ³²P and tritium) or with a detectable agent (e.g., a contrastagent sensitive to a selected wavelength in the visible or infra-redrange); or derivatized (e.g., deoxyglucose, or phosphoinositol). Solutesmay thus be covalently linked to exogenous contrast agents; when linkedto a detectable agent, either the solute or the agent may be measured ormonitored according to the methods disclosed herein. For example, awavelength may be selected such that a contrast agent is substantiallynon-absorbing, or a solute is substantially non-absorbing, or both.

Other features and advantages will become apparent from the followingdescription and from the claims.

DESCRIPTION

FIG. 1 is a diagrammatic side view of a monitor attached to the arm of apatient for monitoring the concentration of one or more solutes in thepatient.

FIG. 1A is a diagrammatic sectional view of the monitor of FIG. 1 takenalong the line IA-IA.

FIG. 1B is a diagrammatic side view of the monitor shown in FIG. 1A.

FIG. 1C is a block diagram of the monitor of FIG. 1.

FIG. 1D is a schematic diagram of a circuit corresponding to a sectionof a sequencer.

FIG. 2 is a plot of intensity as a function of time at two differenttime periods (T₀, T₁) during which the solute concentration levelincreased from C₀ to C₁.

FIGS. 2A and 2B are plots of optical density (OD) as a function ofdetector-light source separation (ρ) corresponding to the time periods(T₀, T₁) of FIG. 2.

FIG. 3 is a plot of a calculated variation of the absorption coefficient(μ_(a)) as a function of source-detector separation (ρ).

FIG. 3A is a plot of a calculated variation of the absorptioncoefficient (μ_(s)′) as a function of source-detector separation (ρ).

FIG. 4 is a flow diagram of a method for monitoring soluteconcentration.

FIGS. 5 and 5A are diagrammatic side views of a calibration model and amonitor used for obtaining a calibration scale, respectively.

FIG. 6 is a table indicating the optical effect of intralipidconcentration upon glucose in the concentration range of 160 mM.

FIG. 7 is a plot of optical density (OD) as a function of input-outputseparation (ρ).

FIG. 7A is a plot of the slope and intercept extrapolated from the plotof FIG. 7 as a function of glucose concentration.

FIG. 8 is a schematic plot of the time course of a solute addition tothe perfusate of rat liver.

FIG. 8A is a plot of optical density (OD) as a function of input-outputseparation (ρ) illustrating the effect of mannitol upon the absorptionof perfused liver (37° C.)

FIG. 8B is a plot of the slope of the OD plot of FIG. 8 as a function ofmannitol concentration.

FIG. 9 is a flow diagram of a scheme for indicating to a patientmeasured solute concentration.

FIG. 10 is a table of baker's yeast as a scatterer and various solutes.

FIG. 11 is a table indicating the optical effect of a variety ofsolutes.

FIG. 12 is a schematic diagram illustrating the difference in volumefraction of scattering particles between a scatterer suspension (a) andtissue or blood (b).

FIGS. 13(a)-(b) are a simulation of the reduced scattering coefficient,μ_(s)′, for a 0.5% Intralipid-glucose suspension (a) and a perfusedliver (b).

FIGS. 14(a)-(c) are plots of time-domain experimental results of a 0.5%Intralipid-mannitol suspension measured at 830 nm.

FIGS. 15(a)-(b) are plots of experimental results, measured with thecontinuous-wave method, of a 0.5% Intralipid-yeast-mannitol suspension.

FIGS. 16(a)-(b) are a simulation of the reduced scattering coefficientμ_(s)′, for a perfused liver, based on equation (12), with morerealistic conditions.

FIG. 16(a) is a plot of the increase of μ_(s)′ with a decrease in sizeof the liver cells (top scale) or with an increase in glucoseconcentration (bottom scale) in the perfusate.

FIG. 16(b) is a plot of the cell radius while the extracellularrefractive index and the cell volume fraction are both fixed.

FIGS. 17(a)-(b) are plots showing the temperature-dependent pathlengthchange of a perfused rat liver for a cooling process (a) and warming-upprocess (b). The data were obtained by the frequency-domain method.

FIGS. 18(a)-(c) are plots of pathlength changes of a perfused rat liverwith 200 mM glucose (a), 200 mM mannitol (b), and 200 mM sucrose (c), inthe perfusate.

FIG. 19 is a plot of experimental results of the absorption coefficientμ_(a) (a), the reduced scattering coefficient μ_(s)′ (b), and meanoptical pathlength (c) of a rat liver perfused with 100 mM sucrose.

FIG. 20 is a PMS scattering change trace at 816 nm.

Referring to FIG. 1, a monitor 10 is attached to the surface of abiological system 12 (e.g., the arm of a patient) for non-invasivelymonitoring the concentration of one or more solutes (e.g., glucose) inthe patient by using a novel optical technique. Monitor 10 is attachedto the patient's arm by an adhesive bandage 14, although other means ofattachment may be used (e.g., a stretchable arm wrap). Monitor 10 may beattached to other regions of the patient's body, e.g., head, breast,finger or belly, depending on the solute to be monitored and, e.g., thecomfort level of the patient. Preferably the location of the monitor isselected to be where the extravascular solute level equilibrates withnearby blood vessels at a relatively rapid rate.

Monitor 10 uses a continuous light method and comprises a singledetector DC amplifier system. This monitoring scheme has producedresults that are compatible in sensitivity to those achievable byfrequency-domain and time-domain methods. The signal-to-noise level ofthe changes observed with continuous light is ˜0.01 milli OD at 850 nmwith a 0.2 Hz bandwidth.

Referring to FIG. 1A, in a presently preferred embodiment, monitor 10includes three spaced-apart light sources (L₁, L₁ and L₃; e.g., 8 voltflashbulbs) and a detector (D₁; e.g., a silicon photodiode). The lightsources are respectively spaced different distances (ρ₁, ρ₂ and ρ₃,respectively) from the detector. For example, in the embodiment shown,ρ₁, ρ₂ and ρ₃ are equal to 7 cm, 5 cm and 3 cm, respectively.

The light sources deliver light into the patient's arm in sequence,which is controlled by a sequencer 15, and the delivered light migratesthough a region of the patient's arm to the detector along one or morepaths that can be respectively characterized by average path lengths 16,18, 20. The distances between the light sources and the detector (ρ₁, ρ₂and ρ₃) are respectively representative of these average path lengths.The lamp spacings from the detector may be varied, depending, e.g., onthe size of the monitored region and on intrinsic noise levels. Incertain preferred embodiments, the lamps should be spaced far enoughapart to take advantage of the spacing effect and thus enhance themeasurement accuracy. Although, in certain applications it is preferredthat the lamps be spaced from the detector by at least 2 cm to achieve asimplification in the mathematics used to derive the soluteconcentration.

As shown in FIGS. 1B and 1C, light received by detector D₁ first passesthrough an interference filter 22 having a passband corresponding to awavelength of 850 nm. In the presently preferred embodiment, theinterference filter is manufactured by Omega, Inc., and the siliconphotodiode beneath it is Part No. F1227-66BR, available from Hamamatsu,having a large sensitive area for favorable signal to noise ratio and anNIR wavelength sensitivity. The sensitive area of the photodiode isapproximately 6 mm². The silicon diode detector is connected to anamplifier 24 that is connected to a recorder 26 to give an intensitytrace 28 as a function of time representative of the signals passingthrough a region of the patient's arm from the three light sources.Amplifier 24 drives the recorder with provision for offset of the zeropoint by adjustment of a potentiometer 25.

The three light sources are sequenced between the three sources at 20sec. for each one. Light sequencer 15 contains three rheostats, whichare adjusted to equalize the signals from the three lamps to give equalsignal to noise ratios. The sequencer also contains three LED's 36, 38,40 to indicate which lamp is sequenced. The sequencer applies not onlythe sequences to the three lamps but also flashes each light source onand off every half second so that a sample and hold circuit can monitorthe difference between the light and dark signals. In this way, astability of approximately 1×10⁻⁵ optical density (OD) and a noise levelof 0.1 of this is obtained with a response time of 1-2 seconds. In oneembodiment, sequencer 15 is an independent source for determining thefrequency of lamp flashing. Lamps flash at frequency of ½ Hz or 2flashes per second or greater. In operation, one lamp flashes, thesignal is picked up by the photodetector and while the lamp is on theintensity is measured and stored on the chart recorder or in computermemory.

All the data is acquired and compared with a chart recorder 26, and thezero value established with the light-off condition. The output ofamplifier 24 may alternatively be sent to an electronic display unit(e.g., an LCD display). The analog signal from amplifier 24 may bedigitized in the display unit and displayed as a digital number. Thesignal is also sent to a comparator (e.g., a computer) for comparing themeasured light intensities from different source-detector positionsagainst a predetermined calibration scale to provide a measure of soluteconcentration.

The three rheostats are adjusted to ensure that the signal intensitiesdetected from the three light sources are equal during a calibrationmode, described below. Thus, abscissa of the plots shown hereincorrespond to the base line obtained for the scatterer only condition(i.e., equal signals from all 3 light sources). The signal obtainedduring the calibration mode is termed I₀. The recorder gain may beincreased to a desired level to obtain a desired sensitivity level,e.g., by factors of 2, 5, or 10. The measured signals are multiplied bythis factor (i.e., 200, 500, 1000). Deflections of the three signalscaused by changes in solute concentration are calculated as a percentageof the initial value (I₀) and multiplied by 0.00434 to convert to log₁₀for absorbency changes of less than 10% (ΔOD). Otherwise, log₁₀ iscomputed.

Referring to FIG. 1D, sequencer 15 enables correction for the darkcurrent/noise that comprises background light, DC offset of theoperational amplifiers, photodiode dark current, temperature effects onthe outputs of individual components and variations due to changingenvironment. The dark current/noise correction is explained inconnection with a circuit 40. Monitor 10 performs data acquisition infour steps which are synchronized by the sequencer. In the first step,the lamps are off. The output of the detector is directed to anintegrator 42 and an integration capacitor 44 is charged to the darklevel voltage. In the second step, one of the lamps is turned on. Thepreamplifier output that corresponds to the intensity of the detectedlight is directed to integrator 42 in a way to charge capacitor 44 withcurrent of polarity opposite to the polarity of the charging current inthe first step. This is achieved using appropriate ON/OFF combination ofswitches S1 and S2. The voltage of capacitor 44 is charging to a valuewhich, at the end of this step, represents the total signal minus thedark level noise signal. In the third step, both switches S1 and S2 areturned OFF to disconnect both the positive unity gain and the negativeunity gain operational amplifiers (46 and 48). Then, the output ofintegrator 42 is moved via switch S3 to a hold circuit 50 which alsofunctions as a low pass filter. This output is the detected signalcorrected for the background noise. In the fourth step, the switches S1,S2 and S3 are open and switch S4 is closed in order to dischargecapacitor 156 through a 47K resistor. At this point, the circuit ofintegrator 154 is reset to zero and ready for the first step to beapplied to the next lamp in the sequence.

In an alternative embodiment, the RUNMAN™ system described inInternational Publication No. WO 92/20273, filed May 18, 1992, which isherein incorporated by reference, may be used to detect the lamp signalsmigrating through the biological system. In this embodiment, the RUNMAN™system is configured as described above and modified for singlewavelength measurement (e.g., 850 nm).

As shown in FIGS. 2-2B, the measured results are plotted as opticaldensity (OD) as a function of light source separation (ρ₁, ρ₂ and ρ₃).The OD is defined as $\begin{matrix}{{{OD} = {\log\quad\left( \frac{I_{0}}{I} \right)}}\quad} & (1)\end{matrix}$where, I₀ is the calibrated initial intensity and I is the detectedintensity, which varies over time in this example as shown in FIG. 2.The plots of OD versus ρ are linear for values of intralipid up to 1%(as discussed in detail below) and may show a non-linearity above thatvalue for the largest detector light-source separation. In such a case,the smaller separations are used.

The best straight line or computer fit (e.g., by minimizing least meansquare error) to the three data points for each measurement period (T₀,T₁) gives the slope in OD per solute concentration (usually 1millimolar), and the extrapolation of the line to the ordinate gives theintercept. In some cases, a two-point slope is calculated (e.g., whenonly two sources are used, or when a data point corresponding to thelargest source-detector spacing is subject to severe nonlinearity).

Similar plots of the variation of slope and intercept with solute andscatterer concentration are made, from which the final measures, namelyOD per millimole solute per percent intralipid or per degree C. arecomputed (as described in detail below). This gives the sensitivityparameter employed in this study.

Theory

According to diffusion theory, the intensity of continuous lightremitted through a semi-infinite scattering medium, such as tissue,depends on the tissue absorption and scattering properties (μ_(a) andμ_(s)′). The detected signal I(ρ), at a separation of p from the sourcecan be given as $\begin{matrix}\begin{matrix}{r_{1} = {\sqrt{\left( \frac{1}{\mu_{t}^{\prime}} \right)^{2} + \rho^{2}} \cdot}} \\{r_{2} = {\sqrt{\left( \frac{{\frac{4}{3}4} + 1}{\mu_{t}^{\prime}} \right)^{2} + \rho^{2}} \cdot}} \\{\mu_{t}^{\prime} = {\mu_{a} + {\mu_{s}^{\prime} \cdot}}} \\{\mu_{eff} = {\sqrt{3{\mu_{a}\left( {\mu_{a} + \mu_{s}^{\prime}} \right)}}.}}\end{matrix} & (2)\end{matrix}$and A is a parameter dependent upon the refractive index of the tissueand the initial light source intensity. When the source detectorseparation is larger than 2 cm, this equation can be simplified as$\begin{matrix}{{I\quad(\rho)} = {\frac{1}{a\quad\mu_{t}^{\prime}}\left( {\mu_{eff} + \frac{1}{\rho}} \right)\frac{{\mathbb{e}}^{{- \mu_{eff}}\rho}}{\rho^{2}}}} & (3) \\{{\ln\quad\left\lbrack {\rho^{2}I\quad(\rho)} \right\rbrack} = {{{- \mu_{eff}}\rho} - {\ln\quad\left\lbrack {a\quad\mu_{t}} \right\rbrack} + {\ln\quad\left\lbrack {\mu_{eff} + \frac{1}{\rho}} \right\rbrack}}} & (4)\end{matrix}$

By having a calibration model with known values of μ_(a)(cal) andμ_(s)′(cal), we can compare an unknown sample to it, based on$\begin{matrix}{{{\ln\quad\left\lbrack {\rho^{2}I_{0}\quad(\rho)} \right\rbrack} - {\ln\quad\left\lbrack {\rho^{2}I\quad(\rho)} \right\rbrack}} = {{\rho\quad\left\lbrack {\mu_{eff} - {\mu_{eff}({cal})}} \right\rbrack} + {\ln\quad\left\lbrack \frac{\mu_{t}}{\mu_{t}({cal})} \right\rbrack} + {\ln\quad\left\lbrack \frac{{\mu_{eff}({cal})} + \frac{1}{\rho}}{\mu_{eff} + \frac{1}{\rho}} \right\rbrack}}} & (5)\end{matrix}$If the unknown and calibration samples have a small difference inoptical properties, the last term of Eq. (5) can be negligible.Therefore, we can define the optical density such that $\begin{matrix}{{OD} = {{\log\quad\left( \frac{I_{0}}{I} \right)} = {{m \cdot \rho} + b}}} & (6)\end{matrix}$where m is the slope and b is the intercept of the OD versus ρ line,given by: $\begin{matrix}\begin{matrix}{m = {\sqrt{3}\quad\left( {\sqrt{\mu_{a}\mu_{s}^{\prime}} - \sqrt{{\mu_{a}({cal})}\quad{\mu_{s}^{\prime}({cal})}}} \right)}} \\{b = {\log\quad\left( \frac{\mu_{a} + \mu_{s}^{\prime}}{{\mu_{a}({cal})} + {\mu_{s}^{\prime}({cal})}} \right)}}\end{matrix} & (7)\end{matrix}$where μ_(a)(cal) and μ_(s)′(cal) are the absorption and reducedscattering coefficients of the calibrated sample and μ_(a) and μ_(s)′are the absorption and reduced scattering coefficients of the sample tobe monitored. By measuring OD versus the source detector separation, wecan obtain slope (m) and intercept values (b). With the measured valuesof slope and intercept, we can obtain values for μ_(a) and μ_(s)′ bysolving Eq. 7 as follows. $\begin{matrix}{\begin{matrix}{\mu_{a} = {\frac{1}{2} \cdot \left( {y - \sqrt{y^{2} - {4x}}} \right)}} \\{\mu_{s}^{\prime} = {\frac{1}{2} \cdot \left( {y + \sqrt{y^{2} - {4x}}} \right)}}\end{matrix}{{where},}} & (8) \\\begin{matrix}{x = {{\mu_{a}\mu_{s}^{\prime}} = \left\lbrack {\frac{m}{\sqrt{3}} + \sqrt{{\mu_{a}({cal})} + {\mu_{s}^{\prime}({cal})}}} \right\rbrack^{2}}} \\{y = {{\mu_{a} + \mu_{s}^{\prime}} = {\left\lbrack {{\mu_{a}({cal})} + {\mu_{s}^{\prime}({cal})}} \right\rbrack\quad 10^{b}}}}\end{matrix} & (9)\end{matrix}$

Eq. (6) exhibits a linear relationship between OD and thesource-detector separation (ρ). The slope and intercept of this equationare studied here by measuring OD versus ρ.

FIG. 3 shows a calculated result of OD versus source-detector separationas a function of absorption change of the measured sample. Thecalibration sample used here has μ_(a)(cal) and μ_(s)′(cal) values of0.1 cm⁻¹ and 10 cm⁻¹, respectively, indicated by the standard horizontalline in the figure.

FIG. 3A gives the slope and intercept dependence on the scatteringproperty of the measured sample for the same calibrations. Above μ_(s′),=10 cm⁻¹, the slope and intercept are of equal sensitivity, while theintercept is more sensitive below μ_(s)′, =10 cm⁻¹. FIG. 3A shows thatthe slope and intercept are negative if μ_(s)(sample)<μ_(s)′(cal), andthe slope and intercept are positive if either μ_(s)(sample>μ_(a)(cal).Therefore, by determining the slope and intercept of OD versussource-detector separation, one can characterize the absorption andscattering properties or changes of an unknown sample with respect tothe calibration sample, i.e., a relative μ_(a)μ′_(s) is determined, ascontrasted to frequency-domain or time-domain studies.

Referring to FIG. 4, the concentration of one or more solutes in abiological system, e.g., a patient, may be monitored by the followingprocess. Obtain calibration values μa(cal) and μ_(s)′(cal) correspondingto the intrinsic absorption and reduced scattering coefficients for apatient (step 60). These calibration values may be obtained using wellknown optical techniques (e.g., TRS or PMS) and need only be determinedonce for a given patient. These calibration values vary from patient topatient due to variations in skin pigmentation, variations inthicknesses of different skin layers, etc. Measure the so-called initialintensity I₀ for the patient under conditions that will be consideredreference conditions (e.g., when the patient's biological systems areoperating normally) (step 62). This initial intensity is used as thereference intensity for determining the determined optical density (OD;Eq. 1). Monitor the concentrations of one or more solutes in the patientby measuring the intensity (I) detected by the system described abovefor at least two different source-detector spacings (ρ) (step 64). Theintensity (I) can then be used to determine a best linear fit to the atleast two (OD, ρ) data points. Extrapolate slope (m) and intercept (b)values from the measured (OD, ρ) data points (step 66). Compare theextrapolated slope (m) and intercept (b) values against a predeterminedcalibration scale (e.g., as described below) to obtain a measure ofsolute concentration (step 68).

This monitoring process is preferably implemented in hardware (e.g., anASIC) or as a software program run on a computer or other processor.

Calibration Scale

A calibration scale for relating the slope and intercept data monitoredusing the above-described technique to obtain a measure of one or moresolute concentrations can be derived from measurements of a simulatedbiological environment or actual biological tissue.

According to a recent study by Graaff et al., (R. Graaff, et al., Appl.Opt. 31(10), 1370-1376 1992), the Mie theory can be well approximated togive the following expression for the reduced scattering cross section,δ_(s)′. $\begin{matrix}{\sigma_{s}^{\prime} = {{\sigma_{s}\left( {1 - g} \right)} = {3.28\quad\pi\quad{a^{2}\left( \frac{2\quad\pi\quad a}{\lambda} \right)}^{0.37}\left( {\frac{n_{i\quad n}}{n_{ex}} - 1} \right)^{2.09}}}} & (10)\end{matrix}$where δ_(s) is the scattering cross section, g is the average cosine ofthe scattering angle, a is the radius of the scattering particle, λ isthe wavelength of the scattered light, n_(in) and n_(ex) are refractiveindexes of the intracellular and extracellular fluid, respectively. Inthe case of model or cell suspension systems, n_(in) and n_(ex)represent refractive indexes of the scattering particle and suspensionsolution, respectively. Three restrictions for validation of equation(10) are a) g factor has to be larger than 0.9 (g>0.9); b) the particleradius and wavelength of scattered light satisfies 5<(2πa/λ)<50; c) therefractive index relative to the surrounding medium is limited in therange of 1<n_(in)/n_(ex)<1.1. With the use of near-infrared light, thesethree conditions are satisfied for scattering in living tissues andblood, (R. Graaff, et al., 1992).

In a highly multiple-scattering medium, the reduced scatteringcoefficient, μ_(s)′, is related to δ_(s)′ by μ_(s)′=λδ_(s)′, where λ isthe total number of the scattering particles per unit volume, (A.Ishimaru, Wave Propagation and Scattering in Random Media, AcademicPress, Inc. San Diego, 1978). This number density, λ, can be given asφ/v_(par), where φ is the volume fraction of the particles relative tothe total volume, and v_(par) is the volume of a single scatteringparticle, (B. Beauvoit et al., Biophys. J. 67, 2501-2510 1994), and canbe expressed as4/3πa³for a spherical scatterer. Substituting δ_(s)′ by equation (10), we have$\begin{matrix}{\mu_{s}^{\prime} = {{\frac{\phi}{v_{par}}\sigma_{s}^{\prime}} = {\frac{2.46}{a}{\phi\left( \frac{2\quad\pi\quad a}{\lambda} \right)}^{0.37}\left( {\frac{n_{i\quad n}}{n_{ex}} - 1} \right)^{2.90}}}} & (11)\end{matrix}$This equation is valid for sufficiently small φ (φ<0.2), such as in cellor scatterer suspensions. For φ<0.5, which is very common for scatterersin tissue and blood, the scattering particles are densely packed, andthe whole solution may be viewed as a homogeneous medium with thescattering particles made of the inter-particle space. These two casesare schematically illustrated in FIGS. 12(a) and 12(b), respectively. Inthe limit of φ−<1, the inter-particle space disappears and μ_(s)′ shouldapproach 0. Based on this consideration, we employ the strategydeveloped by Ishimaru (A. Ishimaru, 1978) and others (L. Reynolds etal., Appl. Opt. 15, 2059-2067, 1967), (J. M. Steinke et al., Appl. Opt.27, 4027-4033, 1988) for red blood cells and give the following modifiedexpression of μ_(s)′ for biological tissues: $\begin{matrix}{\mu_{s}^{\prime} = {{\frac{\phi\left( {1 - \phi} \right)}{v_{par}}\sigma_{s}^{\prime}} = {\frac{2.46}{a}{\phi\left( {1 - \phi} \right)}\left( \frac{2\quad\pi\quad a}{\lambda} \right)^{0.37}\left( {\frac{n_{i\quad n}}{n_{ex}} - 1} \right)^{2.09}}}} & (12)\end{matrix}$Both equations (11) and (12) show that μ_(s)′ has both arefractive-index-dependent factor,$\left( {\frac{n_{i\quad n}}{n_{ex}} - 1} \right)^{2.09}$and a size-dependent factor, either$\frac{\phi}{a}\left( \frac{2\quad\pi\quad a}{\lambda} \right)^{0.37}$for suspensions or$\frac{\phi\left( {1 - \phi} \right)}{a}\left( \frac{2\quad\pi\quad a}{\lambda} \right)^{0.37}$for tissue.

The diffusion approximation of transport theory has been widely used asthe theoretical basis to describe light propagation within a highlyscattering medium for a given geometry [18] (E. M. Sevick et al., Anal.Biochem. 195, 330-351, 1991) and [19] (S. R. Arridge et al., Phys. Med.Biol. 37, 1531-1560, 1992). The solution of the time-domain diffusionequation allows to calculate the mean optical pathlength, <L>, of lighttraveled before detection by <L>=c<t>, where c is the speed of lighttraveled in a mean time, <t>, in the scattering medium. In asemi-infinite, reflectance geometry, <t> can be given as $\begin{matrix}{< t>=\frac{\int{{R\left( {\rho,t} \right)}t{\mathbb{d}t}}}{\int{{R\left( {\rho,t} \right)}{\mathbb{d}t^{\prime}}}}} & (13)\end{matrix}$where R(ρ,t) is the reflectance of impulse light detected on the mediumsurface at time, t, and at distance, ρ, away from the light source.After substituting $(ρ t) in <t> and simplifying <t>, we obtain anexpression relating the mean optical pathlength, <L>, to the absorption(μ_(a)) and reduced scattering (μ_(s)′) coefficients by $\begin{matrix}{< L>={\frac{\sqrt{3}}{2}\rho{{\sqrt{\frac{\mu_{s}^{\prime}}{\mu_{a}}}\left\lbrack \frac{1}{1 + \frac{1}{\rho\sqrt{3\quad\mu_{a}\mu_{s}^{\prime}}}} \right\rbrack}.}}} & (14)\end{matrix}$So <L> can be a marker to monitor a change in absorption or scatteringproperties in the medium under study. Further more, the first orderapproximation of eq. (5) is $\begin{matrix}{< L>={{\frac{\sqrt{3}}{2}\rho\sqrt{\frac{\mu_{s}^{\prime}}{\mu_{a}}}} - \frac{1}{2\quad\mu_{a}^{\prime}}}} & (15)\end{matrix}$indicating that an increase in scattering results in an increase inoptical pathlength.Volume Regulatory of Cells and Effect of Solution Composition onNonelectrolyte-Induced Shrinkage

Depending on the species and the tissue type, the volume change of cellsupon exposure to anisosmotic media is subjected to a regulation. Forinstance, if hepatocytes (liver cells) are suddenly exposed to ahypotonic medium, they initially swell, but within minutes they canregain almost their original volumes. This behavior has been namedRegulatory Cell Volume Decrease and is governed by the activation of K⁺and Cl Efflux. On the other hand, if the cells are suddenly exposed to ahypertonic medium, they initially shrink, but within minutes they attainalmost their initial volumes. This behavior has been named RegulatoryCell Volume Increase and is caused by the activation of na⁺ and Clinflux. However, neither the Regulatory Volume Increase nor Decreasecompletely restore the initial cell volume, and the liver cells are leftin either a slightly swollen or shrunken state. In addition, themechanisms of the regulation of the cellular volume at the cellular(nature of ions) and at the molecular level (carriers responsible forions efflux or influx) are different from one tissue type to anotherone, (D. Haussinger et al, Biochim. Biophys. Acta 1071, 331-350, 1991).

In the liver, when hepatocytes are subjected to hypertonic stress by theaddition of a carbohydrate into the extracellular medium, there iseither no or only a partial recovery from the shrunken state dependingon the nature of the carbohydrate. For instance, the time-course of thesorbitol-induced shrinkage does not show any Regulatory Volume increase,(T. Bakker-Grunwald, Biochim. Biophys. Acta 731, 239-242 1983). Incontrast, sucrose and mannitol-induced shrinkage is followed by apartial recovery of the initial volume. These discrepancies have beenexplained by different permeability of the hepatocyte toward the threenonelectrolytes used in the studies. The higher is the cellularpermeability to the sugar, the faster is the equilibration of theosmolarity between the two compartments, and the faster is the recoveryfrom the shrunken state (P. Haddad, et al, Am. J. Physiol. 256,G563-G569 1989), (G. Alpini et al, Am. J. Physiol. 251, C872-C882,1986).

EXAMPLE 1

The layout of the components is illustrated in FIGS. 5 and 5A, whichshows the tissue model as a 10 cm diameter cylinder 70 filled with oneliter of a scatterer (e.g., intralipid). The slopes and intercepts arecomputed per 1% scatterer per millimolar (mM) solute per cm input/outputat 25° (see FIG. 6).

In order to simulate the detection of solute in a breast, brain, orother portion of the human body, we have employed a cylindrical vesselof 10 cm in diameter and 10 cm in height, to which the optical detectoris attached. The vessel is filled with distilled water to whichappropriate concentrations of scatterer, for example, intralipid (0.1-2%by volume) are added. The vessel filled with a scattering medium with nosolute present may be used as the calibration standard for μ_(a) andμ_(s)′. The solute is then added in increasing concentrations as solidor liquid and dissolved or mixed appropriately by the rapid motion ofthe stirrer bar. Dilution of the scatterer is measured by dilatometry.Thus, relationships between absorbency changes due to the solute andscatterer concentrations are obtained.

FIG. 7 illustrates the results of a typical experiment in 1% intralipidas a scatterer with solute additions of 10, 50, 100, etc. grams ofglucose to 1 liter of 1% intralipid. OD decreases as a function of ρ,for 20 mM increments of glucose; both the slope and the intercept areaffected. The errors due to instrument noise are approximately 1×10⁻⁵ ODas compared with the 120 milli-OD scale of the data shown here. In thiscase an approximately linear relationship of OD and ρ are obtainedaccording to Eqs. 6 and 7.

The relation between solute concentration, slope, and intercept(replotted from FIG. 7) is given in FIG. 7A, and the values are given inTable 1; slope and intercept values show 1.5×10⁻⁴ OD and 0.91×10⁻⁴ ODper mM of glucose and a 1 cm separation of input/output for slope.

These obtained values of slope and intercept are used either alone or incombination to provide a calibration scale against which subsequentmeasurements are compared to obtain a measure of solute concentration.

The values of slope are negative as indicated by FIGS. 7 and 7A, and for1% intralipid a value of −1.56±0.037 is given (FIG. 6). The units are10⁻⁴ OD per 1 mM glucose per 1 cm separation. The error of the slope is0.037, and thus, the signal-to-error ratio in the determination of 1 mMglucose would from these data appear to be approximately 50 at 1 cmseparation and correspondingly less at ρ=7 cm. It is noted that theappropriate coefficient of Eqs. 6 and 7 involves the square root ofconcentration.

The sensitivity, however, varies with the scatterer concentration, andthus the experiment was repeated from 0.1%-1.5% of intralipid, and a newsensitivity constant, reduced to 1% scatterer concentration, is given inFIG. 6 (Table I) to be 1.56×10⁻⁴ OD per 1 mM glucose per 1 cm separationper 1% intralipid. The square root relationship of Eqs. 6 and 7 isfollowed from 20 to 100 mM glucose, and the intercept follows alogarithmic relationship with a value of 90×10⁻⁴ OD per cm per In 1 mMglucose. The values of the intercept increase with increasing intralipid1.4+0.3×10⁻⁴ OD/cm/1 mM glucose per intralipid %.

To monitor temperature variations, the vessel containing a solute (e.g.,glucose) and scatterer (e.g., intralipid) is chilled to 20° C., and thetemperature is slowly ramped to 35° C. by an electric hotplate (uponrapid stirring) and the optical effects are recorded. The scatterer isstirred by a magnetic bar, and the temperature is regulated by theheater/thermostat so that temperatures between 20 and 30° C. can beemployed. The temperature of the system is measured by a mercurythermometer.

EXAMPLE 2

Male SD strain rats, weighing 250-300 g were used. After anesthetizing arat by intraperitoneal injection pentobarbital (50 mg/kg weight), theliver was removed and perfused by Krebs-Ringer buffer containing 2 mMglucose. The buffer was oxygenated by the gas mixture 95% oxygen and 5%carbon dioxide. The liver was placed on an array of light sources and adetector with the separation of 1-3.3 cm. After liver perfusion becamestable (20-30 minutes), the perfusate was changed to others containingdifferent concentrations of glucose or mannitol. The oxygenconcentration of outflow was simultaneously measured.

Precautions are necessary to ensure that the variations of the opticalproperties of the liver itself do not cause optical artifacts. Thus, theperfusion with solute is preceded and followed by control intervals. Thelobes of the rat liver are laid upon an array of light sources anddetectors similar to that indicated in FIGS. 1-1D, but with spacings of1, 2 and 3 cm (and also 1.2, 1.5, and 2.2 cm) to account for the higherabsorbance of the liver and the smaller size of the liver. Furthermore,the thickness of the lobe is approximately 2 cm and the tissue boundaryconditions differ from the model of FIGS. 5 and 5A. We have chosenmannitol as the appropriate solute as contrasted to glucose in view ofits negligible metabolic activity.

A typical trace for the perfusion with 60 mM mannitol is shown in FIG.8. The initial phase of absorbance increase is attributed to the entryof the mannitol into the sinusoids of the liver creating osmoticgradient, which equilibrates over the next 5 minutes. Thereafter, theabsorbance change is assumed to be due to the equilibration of themannitol with liver hepatocytes. In order to ensure that no remnanteffect on the liver has occurred, the perfusate without solute isrestored; the liver is reperfused with crystalloid in the absence ofadded mannitol. In this case, a decrease of absorbance occurs due toeffusion of the mannitol from the tissue spaces, and thereafter theinitial base line is restored. The mannitol effect is then measured asan early phase and a late phase, with respect to the two control levels.

As shown in FIG. 8A, OD versus ρ plots are obtained. These are much“noisier” than the intralipid and yeast cell models, probably due toosmotic and perfusion pressure effects. First, the sign of the early andlate phases is similar. The slope of the early phase corresponds to a+18×10⁻⁴ OD per one mM of mannitol per cm separation of input/output.The late phase corresponds to +1.7×10⁻⁴ OD per mannitol per cm.

EXAMPLE 3

Changes in absorption, scattering coefficients, and optical pathlengthdue to the introduction of a solute in suspensions or in rat livertissue were shown using time-domain, frequency-domain, andcontinuous-wave methods. These three methods measure optical propertiesof highly-scattering medium, transient response of mean pathlengthchange, and fast response to a change in optical properties andscattering changes, respectively. Wavelengths used were in the range of780-850 nm.

In lipid or cell suspension measurements, a cylindrical container (17 cmdiameter, 10 cm height) was filled with distilled water and variousconcentrations of a scattering medium. Intralipid (Kabi Pharmatica,Clayton, N. Dak.), with a 20% concentration, was diluted to 0.5-2.5%(vol/vol). In the case of cell suspensions, a slurry of either 1.4% or2.8% by weight of baker's yeast in 20 mM phosphate buffer, pH 7, wasadded to the lipid solution. During measurements, optical properties(absorption, reduced scattering coefficients) were altered by titrationof 50 nM of solutes such as glucose and mannitol. The light source anddetector, connected to a NIR detection system such as those describedabove, were placed 3 cm above the suspension surface or from the side ofthe container.

Male SD strain rats (300-350 grams) were starved 24 hours to normalizeliver physiological conditions. After anesthetizing each rat with a 50mg/kg body weight intraperitoneal injection of pentobarbital, the ratliver was removed and perfused by Krebs-Ringer buffer (2 mM glucose,oxygenated by gas mixture of 95% oxygen and 5% carbon dioxide) untilperfusion became stable (20-30 min.). The perfusate was switched betweenbuffer and buffer solutions containing different concentrations ofcarbohydrates. The separation between light source and detector, whichwere attached to the major lobes of the liver, was 1.5 cm.

In simulations, equations (12) and (13) were used for the suspension andtissue cases, respectively, to calculate changes in reduced scatteringcoefficient under various conditions.

EXAMPLE 4

A non-invasive determination of potassium effusion within the brain ofan (in vivo) animal model was demonstrated. The effusion of potassiumfrom an hypoxic rat brain was measured as a light scattering change at816 nm, a wavelength that is relatively indifferent to theoxygenation/deoxygenation of hemoglobin. The diagram FIG. 19 shows acalibration with a sucrose load in the brain which increased potassiumion concentration in the interstitial or extracellular space (and thus,light scattering). Injection of the anesthetic ketamine caused littlelight scattering change. When the rat was exposed to nitrogen gas(breathing), the initial scattering change is in the same direction assucrose infusion, but was due to leakage of potassium from the neurons.Upon restoration of metabolic activity, a large overshoot appeared whichsubsided to baseline levels after several minutes. Light scattering wasshown to demonstrate the functional state of the animal brain. Sincephoton migration in the human brain has been shown to be readilyobservable, the disclosed technique can be applied to patients who haveconditions such as stroke, eschemia, head trauma, brain bleeds, coma,and other conditions known to those in the art to ascertain the generallocation of the injury (e.g., stroke) and the tissue volumes in whichoxygen and hence energy is lacking. Correlation between the opticalproperties of tissue and tissue refractive index

a) Simulation Results:

Based on equation (11), the dependence of reduced scatteringcoefficient, μ_(s)′, of suspension models on the refractive index ofscattering particles (n_(in)) and suspension fluid (n_(ex)) can becalculated assuming that the size and the volume fraction of thescattering particles do not change. FIG. 13(a) shows μ_(s)′ values of a0.5% Intralipid-glucose suspension as a function of added glucoseconcentration and corresponding refractive index of the lipidsuspension, n_(ex). The parameters used in this case are a=0.25 μm,φ=0.005, λ=800 nm, n_(in)=1.465, and n_(ex)=1.325+2.73×10⁻⁵x[C], where[C] is the glucose concentration in MM (Maier et al. Opt. Lett. 19(24),2062-2064 (1994)). On the other hand, we use equation (12) to simulateμ_(s)′ changes of a perfused rat liver as a function of added glucoseconcentration; the results are shown in FIG. 13(b). This calculationvaries only the refractive index of the extracellular fluid asn_(ex)=1.33+2.73×10⁻⁵x[C] and keeps other parameters constant (a=10.68μm, φ=0.8, λ=800 nm, and n_(in)=1.465) (Beauvoit et al Biophys J. 67,2501-2510 (1994)). The initial μ_(s)′ value of 15.9 cm⁻¹ at 0 mM glucoseconcentration is based on a published, experimentally-measured data(1994). This dependence of μ_(s)′ of the liver on the glucoseconcentration assumes that the liver cells are rigid. Both FIGS. 13(a)and 13(b) illustrate that if addition of glucose/carbohydrate insuspension models or in tissue, such as in perfused rat liver, does notchange the size of the scatterers or cells, the reduced scatteringcoefficient, μ_(s)′, of the corresponding system decreases as the addedglucose concentration increases.

b) Experimental Results in Lipid and Cell Suspension Models:

FIG. 14 plots a set of time-domain experimental results of 0.5%Intralipid suspension as a function of nammitol concentration added intothe suspension at a wavelength of 830 nm. By fitting the time-resolvedspectroscopy data, we can obtain the values of mean optical pathlength,μ_(s)′, and μ_(a), as plotted in FIGS. 14(a), 14(b), and 14(c),respectively. The solid data points in FIG. 14(a) were determined bysubstituting the measured reflectance into equation (13), whereas thedashed line with empty circles was calculated by replacing the fittedμ_(a) and μ_(s)′ values in equation (14). The consistency between thesetwo pathlength determinations confirms the correctness of the fittedvalues of μ_(a) and μ_(s)′. FIGS. 14(a) and 14(b) clearly show that boththe pathlength and the reduced scattering coefficient, μ_(s)′, decreaseas the mannitol concentration added in the suspension increases. FIG.14(b) is in a good agreement with the simulation result shown in FIG.13(a). FIG. 14(c) illustrates a very small decrease in μ_(a) value whilethe mannitol concentration becomes larger. Very similar results havebeen obtained for glucose titration (not shown) experiments.

We have also used the continuous-wave method to measure solute-inducedchanges of optical properties in lipid/cell suspensions. A variety ofsolutes (electrolytes, nonelectrolytes, sugars, and alcohols) has beenstudied, and some of the results have been reported (Chance et al. Anal.Biochem. 227, 351-362 (1995)). The results obtained with thecontinuous-wave method for the suspension models are very similar tothose with the time-domain method and also similar to the theoreticalcalculations. An example, FIG. 15 shows a relationship of μ_(s)′/μ_(a)versus mannitol concentration for an Intralipid-yeast suspension withmannitol titration.

Correlation Between the Optical Properties of Tissue and Tissue CellVolume

a) Simulation Results:

Since the cell volume fraction, φ, is usually greater than 0.5 fortissues, equation (12) is used in this section. We consider threesituations for the simulations: 1) changes in cell size only; 2) changesboth in cell size and in refractive index of the extracellular fluid;and 3) changes in cell size, cell volume fraction, and refractive indexof the extracellular fluid. The fact that introducing a carbohydrateinto tissue, such as a perfused rat liver, causes cell shrinkage isconsidered in the simulations.

FIG. 16(a) shows the simulated dependence of μ_(s)′ of a perfused ratliver on cell radius (top scale), with fixed parameters of cell volumefraction (φ=0.8), intracellular (n_(in)=1,465), and extracellular(n_(ex0)=1.33) refractive indexes. The chosen value of n_(in) is basedon Refs. 5 and 26, and n_(ex0) is extrapolated from Ref. 14. Thiscalculation illustrates that a decrease only in tissue cell size resultsin an increase in reduced scattering coefficient, μ_(s)′, and thus inpathlength; vice visa. A decrease in cell size may be caused by atemperature increase of tissue or by an addition of a carbohydrate intissue. FIG. 16(a) also gives the dependence of μ_(s)′ on glucoseconcentration (bottom scale) introduced into liver, having arelationship of a=a₀−k[C], where a is the cell radius, a₀=10.678 μm isthe initial cell radius without any glucose addition, k=0.002 is aconstant, and [C] is the glucose concentration. The k value correspondsto a factor that gives a decrease of 5% cell volume for each 100 mMglucose addition in liver.

A decrease in cell size can lead to a decrease in cell volume and thusin cell volume fraction, φ, since $\phi = {\frac{V_{cell}}{V_{total}}.}$Therefore, an addition of a carbohydrate to tissue can result in adecrease of φ. This occurs when tissue cells shrink but the whole tissuevolume does not change significantly. However, φ# can also remainconstant when the addition of a carbohydrate to tissue results in waterloss in the tissue, causing the total volume, V_(total), to decrease. Tosimulate more realistically μ_(s)′ change upon exposure to acarbohydrate, one considers an overall effect due to all changes in 1)cell size, 2) extracellular refractive index, and 3) cell volumefraction. The solid circles in FIG. 16(b) are calculated for therelationship between μ_(s)′ and added glucose concentration with avariable cell radius, a, and a variable extracellular refractive index,n_(ex), but a fixed cell volume fraction, φ(=0.8). On the other hand,the open circles in FIG. 16(b) correspond to the simulation of μ_(s)′for variable a, n_(ex), and φ with a relationship of${\phi = {4\pi\frac{\alpha^{3}}{3}V_{total}}},$where V_(total) remains constant. Except for φ, other parameters forthese two traces are the same, namely, n_(in)=1.465,n_(ex)=1.33+2.73×10⁻⁵[C], a=10.678−2×10⁻³[C] in μm, and λ=0.8 μm. Thesetwo circle traces show a contradictory behavior of μ_(s)′ as thecarbohydrate concentration increases. After considering all effects ofcell size, extracellular refractive index, and cell volume fraction, weshow from the simulation data that in the addition of asolute/carbohydrate in tissue, the overall scattering of tissue canincrease or decrease depending on if φ decreases or is unchanged,respectively.b) Experimental Results in a Perfused Rat Liver:

To separate the effects of changes in cell size and in extracellularrefractive index on μ_(s)′ due to a carbohydrate addition,temperature-dependent pathlength measurements were performed with thefrequency-domain method (phase-modulation spectroscopy) for a perfusedrat liver. In principle, if tissue temperature is lowered, K⁺ insidetissue cells may come out from the cells, and extracellular water mayenter the cells, leading to cell swelling. It is also known that thetemperature effect on the refractive index of a scattering fluid isrelatively small (1994), so changes in extracellular refractive indexcaused by temperature can be ignored. Then, the overall μ_(s)′ value oroptical pathlength of the swollen cells of a cooled tissue shoulddecrease according to the simulation given in FIG. 16(a) above. On theother hand, if the cooled tissue is warming up, the cells will shrink,and the pathlength will increase accordingly. In the experiment, thetemperature of the liver was altered by changing the temperature of theperfusate, which is contained in a thermally controlled bath. FIG. 17(a)corresponds to a cooling process of the liver from 37° C., the perfusatetemperature measured in the bath, to 25° C. in about 10 minutes. A few(˜2.5) minutes after the perfusate starts to cool down, the liver startsto response, and the pathlength keeps decreasing as the livertemperature goes down until the perfusate temperature stabilizes at thesetting temperature of 25° C. In contrast, FIG. 17(b) shows an increasein pathlength when the perfusate of the perfused liver is warming upfrom 25° C. to 37° C. The time courses for the cooling down (FIG. 17(a))and warming up (FIG. 17(b)) processes are not necessarily the same,mainly depending on the amount of cooling source (ice) and heating powerused. FIG. 17 confirms the simulation results (FIG. 16(a)) that thescattering coefficient of the tissue, and thus corresponding opticalpathlength measured, will increase/decrease with a decrease/increase incell size.

To study coupled effects on μ_(s)′ due to changes in both cell size andrefractive index of the extracellular fluid, several carbohydrates wereadded in the perfusate for the liver perfusion experiments. FIG. 18 is aset of time-dependent curves of pathlength measurements with thefrequency-domain method during the liver perfusion with three kinds ofcarbohydrates. Curves (a), (b), and (c) correspond to a perfusatecontaining 200 mM glucose, 200 mM mannitol, and 200 mM sucrose,respectively. Two traces in curve (b) represent two measurements of twoindividual livers, demonstrating that different livers may be underdifferent physiological conditions and thus have different responserates to mannitol. FIG. 18 shows clearly that the pathlengths or thescattering properties are different in these three cases. The similaritybetween the glucose and mannitol perfusion is that the pathlengthincreases as the carbohydrate perfusion starts. But the pathlength inthe glucose perfusion returns to its baseline much faster than that inthe mannitol perfusion. In contrast to these two perfusions, thepathlength decreases when the sucrose perfusate enters the liver anddoes not return to its baseline until the sucrose starts washed out bythe buffer. To quantify the values of μ_(a) and μ_(s)′, the time-domainmethod was used for another sucrose perfusion, and the results are givenin FIG. 19. It shows that the μ_(s)′ values as well as opticalpathlengths of the liver, perfused with 100 mM sucrose, decrease with asmall variation of μ_(a) during perfusion. The agreement between theresults obtained with the time- and frequency-domain methods confirmsthe correctness of the data.

The data given in FIGS. 13, 15, and 19 show a negligible change of μ_(a)and a consistent increase/decrease between μ_(s)′ and pathlength due toan addition of a carbohydrate in the suspensions or tissue. Theseresults are in good agreement with equation (15). Therefore, we canconclude that an increase/decrease of pathlength measured in tissue dueto a carbohydrate addition reflects an increase/decrease of its overallscattering property.

The simulation and experimental results demonstrate that the reducedscattering coefficient of tissue can be affected largely by the changesin refractive index of the extracellular fluid and in cell volume causedby osmotic stress due to carbohydrate addition to the tissue. However,in the Intralipid-yeast suspension case (FIG. 15), it seems that theeffect of yeast cell variation is not very notable since the result inthis case is very similar to that of the pure lipid suspension. This canbe explained by two reasons: 1) the cell volume fraction relative to thewhole suspension volume is very small; 2) the yeast cells havepolysaccharide walls, which are much more rigid than the regularmembranes of tissue cells. Thus, the cell size and cell volume fractionof yeast cells would not change significantly by the osmotic pressurecaused by the carbohydrate addition in the suspension.

Addition of a solute or carbohydrate into tissue can cause both adecrease in cell volume fraction and an increase in refractive index ofthe extracellular fluid. These two changes contradict each other in theoverall scattering behavior of the tissue. So measurements of opticalpathlength changes can show which factor, cell volume change orrefractive index change, plays more important role than the other. Inthe liver glucose perfusion presented by curve (a) in FIG. 18, thepathlength of the perfused liver increases rapidly and then returns toits original value within 2-3 minutes. This pathlength variationindicates that a decrease in cell size and in cell volume fraction, φ,must occur in the beginning of the perfusion, but soon the shrunkencells regain some of their original volumes. When the washout buffer isswitched on, the pathlength starts to decrease since in this case, thecells are under hypotonic condition so that they start to swell. Again,the pathlength returns to its baseline in 3 minutes when the cellsrecover their initial volumes. The data for mannitol perfusion shown bycurve (b) in FIG. 18 are similar to those in the glucose perfusionexcept that the returning rate to the baseline for mannitol is slowerthan that for glucose. This can be explained by the smaller permeabilityof the liver cells to mannitol than to glucose, so the uptaking rate formannitol is slower than that for glucose.

In principle, neither the Regulatory Volume Increase nor Decrease oftissue cells can regain the initial cell volume completely. It meansthat the pathlength given in curves (a) and (b) of FIG. 18 should notcompletely return to its initial value. However, the change inrefractive index of the extracellular fluid also occurs and compensatesthe effect of the change of cell volume. Thus, the pathlength trace canstay about the baseline, return to the baseline, or go below thebaseline, as demonstrated by the two traces in curve (b), after theinitial prominent response, largely depending on the tissue type andconditions.

The pathlength data for the sucrose perfusion given by curve (c) in FIG.18 is quite different from the other two cases in two aspects: 1) thepathlength decreases when the perfusion starts, and 2) the pathlengthdoes not intend to return to its baseline until the washout buffer isswitched on. It is known that 1) cell shrinkage occurs when the ratliver is perfused with sucrose (Haddad et al., Am. J. Physiol. 256,G563-G569 (1989), 2) the refractive index of sucrose is 1.34783, verysimilar to that of glucose (1.3479) (Windholz et al., The Merck Index:An Encyclopedia of Chemicals, Drugs, and Biologicals, Merck & Co., Inc.,Rahway (1983), 3) the liver cell membrane is impermeable to sucrose(Haddad et al. (1989)). The first two points indicate that the effectscaused by changes in cell size and extracellular refractive index in thesucrose and glucose perfusion of the liver should be very similar. Anexplanation for the opposition pathlength feature in the sucroseperfusion is that the cell volume fraction, φ, remains unchanged in thiscase, behaving differently from that in the glucose perfusion. It hasbeen reported that the liver perfused with sucrose was subjected to alarge amount of water loss (Haddad et al. (1989)). Thus, it is possiblethat both V_(cell), due to cell shrinkage, and V_(total), due to waterloss in tissue, decrease so that φ=V_(cell)/V_(total) remain constant.The impermeability of the liver cell membrane to sucrose can be taken toexplain the non-return feature since in this case, only water movementfrom the intracellular to extracellular compartments is involved,preventing the Regulatory Volume Increase.

Detection in vivo of changes in scattering property owing to glucoseintake on human subjects has been reported (Maier et al. (1994)). Themeasurements were performed on the thigh of the subject, and thescattering factor started to decrease a few minutes after the glucoseingestion, opposing to our results obtained in the liver glucoseperfusion. This inconsistency may be due to the fact that the glucose invivo measurement, performed on the human thigh, may include a largeportion of muscle and blood, whereas the liver perfusion measurementonly involves pure liver cells. Since muscle cells are absolutelynon-spherical and very different from the liver cells in shape andcomposition, muscle cells may response to glucose quite differently fromthe liver cells. On the other hand, if the cell volume fraction does notchange much by the glucose intake, the scattering factor will decreasemainly due to the change in extracellular refractive index. Also whenblood is involved in the measurement, the coupling of uptaking processof glucose by the red blood cells and muscle cells complicates themechanism of changes in scattering property.

These results successfully demonstrate using the NIR techniques fornon-invasive physiological monitoring, such as monitoring tissueswelling by detecting pathlength (i.e., scattering property) change. Forexample, if the pathlength increases, the cells are shrinking. Ifadditions of solutes/carbohydrates are involved, one may encountermultiple effects due to changes in cell size and in extracellularrefractive index. But by using suitable carbohydrates, such as glucoseor mannitol, effects of changes in cell size of tissue can dominate sothat tissue swelling can still be detectable by monitoring thepathlength change.

In summary, the theoretical and experimental results show that additionof a solute/carbohydrate in tissue affects the size of tissue cells, thecell volume fraction, and the refractive index of the extracellularfluid, and thus affects the overall tissue scattering properties. Theapproximated approach of the Mie theory was used to calculate theeffects of osmolarity and refractive index on reduced scatteringcoefficient of tissues and photon diffusion theory was used to associatethe reduced scattering coefficient to the optical pathlength.Experimentally, all of the three NIR techniques are capable of measuringthe changes of optical properties due to an addition of a solute intissue models and in perfused rat livers. The temperature-dependentpathlength measurements of the perfused liver confirmed the dependenceof tissue scattering on the tissue cell size. The liver results obtainedwith three kinds of carbohydrate perfusion display different scatteringaspects which are explained by changes in cell size and volume fraction.

FIG. 12 is a schematic diagram illustrating the difference in volumefraction of scattering particles between a scatterer suspension (a) andtissue or blood (b). In case (a), the volume fraction of the scatterersis φ=0.026, whereas in case (b), the volume fraction of the scatterersis φ=0.73.

FIG. 13 shows simulation results of the reduced scattering coefficient,μ_(s)′, for a 0.5% Intralipid-glucose suspension (a) and a perfusedliver (b). The calculation for (a) is based on equation (2), whereas thecalculation for (b) is based on equation (3). The relationship betweenthe glucose and refractive index for the scattering particle in thesuspension or for the extracellular fluid of the tissue is given in thetext. In case (b), the liver cells are assumed rigid; only therefractive index of the extracellular fluid varies.

FIG. 14 shows time-domain experimental results of a 0.5%Intralipid-mannitol suspension measured at 830 nm. This figure showsmean optical pathlength (a), reduced scattering coefficient μ_(s)′ (b),and absorption coefficient μ_(a) (c) of the suspension as a function ofmannitol concentration added in the suspension.

FIG. 15 shows experimental result, measured with the continuous-wavemethod, of a 0.5% Intralipid-yeast-mannitol suspension. It shows adecrease of the reduced scattering coefficient μ_(s)′ (a) and a relativeconstant of the absorption coefficient μ_(a) (b) of the suspension withan increase in mannitol concentration in the suspension.

FIG. 16 shows the simulation results of the reduced scatteringcoefficient μ_(s)′, for a perfused liver, based on equation (12), withmore realistic conditions. FIG. 16(a) shows an increase of μ_(s)′ with adecrease in size of the liver cells (top scale) or with an increase inglucose concentration (bottom scale) in the perfusate. In FIG. 16(a),the variable is only the cell radius; the extracellular refractive indexand the cell volume fraction are both fixed. The solid circles in FIG.16(b) were obtained by varying cell radius and extracellular refractiveindex. The open circles in FIG. 16(b) were calculated by varying cellradius, extracellular refractive index, and cell volume fration.

FIG. 17 shows temperature-dependent pathlength change of a perfused ratliver for a cooling process (a) and warming-up process (b). The datawere obtained by the frequency-domain method.

FIG. 18 shows experimental results of pathlength changes of a perfusedrat liver with 200 mM glucose (a), 200 mM mannitol (b), and 200 mMsucrose, respectively, in the perfusate. The two traces in case (b) wereobtained from two different rat livers.

FIG. 19 shows experimental results of the absorption coefficient μ_(a)(a), the reduced scattering coefficient μ_(s)′ (b), and mean opticalpathlength (c) of a rat liver perfused with 100 mM sucrose. The datawere determined by the time-resolved spectroscopy. The solid and emptycircles correspond to the measurement at 780 nm and 830 nm,respectively.

Applications

Various solute concentrations may be monitored using the monitoringscheme of the present invention.

EXAMPLE I

The present invention provides is simple, cost-effective, portablescheme for monitoring the concentration of sugars (mannitol, fructose,sucrose, glucose) in a patient. Sensitivities of 1×10⁻⁴ ΔOD per mmol perpercent intralipid at 25° C. have been observed. A comparison with atypical noise level of 10⁻⁵ ΔOD, suggests that the range of 8-12 mM canbe detected satisfactorily.

The glucose concentration in a patient is monitoring according to thisexample by attaching the monitor of FIGS. 1-1D to the patient on thebreast, the belly, the finger, or on the head. The optimum tissue forthis determination is one in which the extravascular glucose level israpidly equilibrated with the blood vessels.

Referring to FIG. 9, in one preferred embodiment of a glucose monitoruseful, e.g., for monitoring the glucose level of a diabetic patient,the patient's blood glucose concentration is detected using the processdescribed above in connection with FIG. 4 (100). In one embodiment, thepatient reads the extrapolated slope and intercept values directly fromthe output of a comparator (e.g., a computer or other processor) andcompares these values to a predetermined calibration scale (describedabove).

In an alternative embodiment, a processor receives the extrapolatedslope and intercept values and compares these values to a predeterminedstored calibration scale. The processor further implements the followingsteps to indicate to the patient the measured solute concentration. Ifthe measured concentration (C_(solute)) is less than a firstpredetermined threshold concentration (C_(th,1)), e.g., 0-100 mmol andmore preferably 50 mmol (step 102), a green signal is output (104),e.g., by lighting a green light, indicating the patient's blood glucoselevel is generally within normal levels. If the measured concentrationis greater than C_(th,1), the measured concentration is compared againsta second predetermined threshold concentration (C_(th,2)), e.g., 50-200mMol and more preferably 120 mmol (step 106). If C_(solute) is less thanthis second threshold concentration, a yellow signal is output (108),indicating that the patient's blood glucose level has risen above normallevels and should be monitored carefully. If C_(solute) is greater thanC_(th,2), a red signal is output (110), indicating that the patientshould attempt to remedy his or her condition.

EXAMPLE II

The alcohol concentration in a patient may also be monitored using thescheme according to the present invention. Ethanol readily equilibrateswith tissue spaces and gives a relatively small but significant signal.Accordingly, a patient (as used herein the term “patient” is used tobroadly refer to a person in general whether or not the person is beingtreated for a medical problem) attaches the monitor of FIGS. 1-1D to thebreast, the belly, the finger, or the head. A processor, as describedabove in connection with Example I receives as input light intensitysignals from a monitor as described in connection with FIGS. 1-1D andimplements the algorithms shown in FIGS. 4 and 9 to provide a measure ofthe alcohol content in the patient's system.

The calibration scales are determined empirically as described above,e.g., in connection with Example 1. The threshold levels (C_(th,1),C_(th,2)) are selected to correspond to desired criteria (e.g., legaldrinking limit).

EXAMPLE III

The concentration of salts (e.g., NaCl, KCl and MOPS) in a patient mayalso be monitored using the scheme according to the present invention.Accordingly, a patient attaches the monitor of FIGS. 1-1D to the breast,the belly, the finger, or the head. A processor, as described above inconnection with Example I receives as input light intensity signals froma monitor as described in connection with FIGS. 1-1D and implements thealgorithms shown in FIGS. 4 and 9 to provide a measure of the alcoholcontent in the patients system. FIG. 10 (Table II) includes data onNaCl, KCl, and MOPS. The effect of these electrolytes is relativelysmall but significant.

The calibration scales are determined empirically as described above,e.g., in connection with Example 1. The threshold levels (C_(th,1),C_(th,2)) are selected to correspond to desired criteria, depending,e.g., on the health of the patient. For example, patient's with highblood pressure would be assigned lower threshold concentrations.

EXAMPLE IV

Enhanced results are achievable if the effects of solute concentrationsother than that which is to be measured can be ignored. According tothis example, the history of the patient is well characterized so thatit can be assumed that variations in the monitored concentration levelare due to variations in the solute concentration that is desired to bemeasured.

For example, an enhanced glucose concentration measurement of a patientis obtained using the monitor described in FIGS. 1-1D, which is coupledto a processor for implementing the steps of FIG. 4, when the patienthas not subjected himself or herself to elevated concentrations of otherscattering solutes, such as alcohol and salts.

In view of the low specificity in solute discrimination, especially thephysiologically important ones, glucose, ethanol, mannitol, and to alesser extent NaCl and KCl, the in vivo studies are undertaken withsupplementary information of the parenteral fluids in use. In addition,the osmotic transients and indeed the osmotic state of the tissue can beof importance, especially in patients undergoing dialysis procedures.Finally, and possibly most important, is the body tissue temperature,which should be monitored in the particular tissue volume studiesoptically, probably by the water absorption.

FIG. 11 (Table III) illustrates the effect of a variety of solutes,mannitol, fructose, and propanediol in the range of molarities up tothat indicated in the table. The slope is normalized in the same way asabove, except it is not divided by the percent of intralipid. The slopevalues are within the experimental error equal to mannitol and fructose.Alcohols and propanediol give a significantly smaller slope per mM and amuch smaller intercept after connection for dilution (see below). Thesmall effect of methanol on yeast cells as a scatterer is noted in TableIV.

At the same time, an appropriate correction for water absorption may beimplemented.

Furthermore, since intensity measurements are especially sensitive tochanges in the skin contact between the probe and the phantom or theprobe and the body tissue makes measurements which do not depend uponintensities vastly preferable, and one of these methods is the phasemodulation system, which surely would be the ultimate system for mostreliable measurements. However, the relationship between the intensitysignal and the phase signal is such that very high phase sensitivitiesare required. The absorbance limitation of 10⁻⁵ may have to be measured,which requires similar accuracies of phase determination.

Other Embodiments

More than three sources may be used to obtain enhanced measurements byobtaining a greater number of data points from which to extract thelinear parameters (slope and intercept).

Instead of using multiple light sources a single source may be used,which applies the light to the biological system from locations spacedfrom the detector by different distances. Alternatively, the singlesource may remain stationary and the detector may be sequentially movedto detecting positions located at different distances from the source.

The monitoring scheme described herein has a relatively small wavelengthdependence. Thus, a dual wavelength method may be used for this purposefor the minimization of hemoglobin crosstalk. In this technique thehemoglobin concentration is quantified by an appropriate phasemodulation spectrophotometer to provide accurate path length informationat the wavelengths involved. Thus, the discrepancy of absorbancemeasurements at 850 nm from the hemoglobin spectrum can be assumed to becounted as pertaining to the solute measurement.

Possible variability of the light entry into the tissue and its arrivalat the detector system consisting of a silicon diode or a fiber coupler(e.g., due to variable tissue contact) may be compensated for byfrequency-domain methods, which may have a significant advantage fortissue contact. The use of several input-output spacings is necessaryfor these determinations. The different spacings sample different tissuevolumes of different depths: the short spacing—shallow and the longspacing—deep tissue volumes. Thus, in cases where heterogeneous tissueis involved, the possibility that different solute levels are sampled atdifferent input-output spacings should be compensated for.

Time-domain methods may alternatively be used. These methods sampledifferent tissue volumes for the calculation μ_(s)′ and μ_(a) (early andlate, respectively). The use of Fourier transformation from time tofrequency domain may rectify this problem. In these frequency-domaindevices, the high frequency waves penetrate shallowly and the lowfrequency deeply. Thus, dual measurements, particularly at a pair ofwavelengths at which the absorption is canceled out, serve as usefulmeans for calculating scattering factor.

Still other embodiments are within the scope of the invention. The abovesolutes can be monitored or their concentration can be measured by atime resolved spectroscopy (TRS) or a phase modulation spectroscopyCPMS). Suitable TRS systems are described in U.S. Pat. No. 5,119,815 or5,386,827, which are both herein incorporated by reference. The TRSsystem employs one or more visible or infrared wavelengths sensitive(i.e., due to variation in absorption or scattering) to the measuredsolute directly or indirectly. The TRS system measures in vivo thevalues of the effective scattering coefficient (μ_(s)′) or theabsorption coefficient (μ_(a)) and correlates these values to aconcentration of the solute.

Alternatively, the measurements are performed using a PMS systemdescribed in U.S. Pat. No. 4,972,331, 5,122,974 or 5,187,672, or inInternational Applications PCT/US94/02764, filed Mar. 15, 1993, orPCT/US92/00463, filed Jan. 21, 1992, all of which are incorporated byreference. The PMS system employs light of one or more visible orinfrared wavelengths sensitive (i.e., due to variation in absorption orscattering) to the measured solute directly or indirectly. The PMSsystem measures in vivo the values of the scattering coefficient (μ_(s))or the absorption coefficient (μ_(a)) and correlates these values to aconcentration of the solute. In addition, quantitation of thespectroscopic signals measured by both the TRS spectroscopy and the PMSspectroscopy are further explained in Sevick et al., AnalyticalBiochemistry, Vol 195, pp. 330-351 (1991), which is herein incorporatedby reference.

The TRS or PMS spectroscopies employ wavelengths that may be directlysensitive to the measured solute, wherein the solute is as defined above(e.g., a metabolic intermediate, a metabolite, an electrolyte, a sugar,the combination of a solute bonded to a detectable agent, such as acontrast agent, or any other component that provides an indirect measureof the solute).

1. A method for monitoring a solute in a biological system comprisingthe steps of: delivering light into a biological system containing saidsolute, said light having a wavelength selected to be in a range whereinsaid solute is substantially non-absorbing; detecting at least first andsecond portions of said delivered light, said first portion havingtraveled through said biological system along one or more pathscharacterized by a first average path length, and said second portionhaving traveled through said biological system along one or more pathscharacterized by a second average path length that is greater than saidfirst average path length; and comparing said first and second portionsof the delivered light to monitor concentration of said solute in saidbiological system.
 2. The method of claim 1 wherein the step ofcomparing said first and second portions of the delivered lightcomprises obtaining a characterization of said biological system basedon a linear model relating an optical characteristic of said biologicalsystem and said first and second average path lengths.
 3. The method ofclaim 2 wherein said characterization that is obtained is the slope of aline determined by fitting to said linear model measured characteristicsof said first and second portions of light and distances representativeof said first and second path lengths.
 4. The method of claim 2 whereinsaid characterization that is obtained is the intercept of a linedetermined by fitting to said linear model measured characteristics ofsaid first and second portions of light and distances representative ofsaid first and second path lengths.
 5. The method of claim 2 whereinsaid characterization that is obtained is the slope and the intercept ofa line determined by fitting to said linear model measuredcharacteristics of said first and second portions of light and distancesrepresentative of said first and second path lengths.
 6. The method ofclaim 2 wherein obtaining a characterization comprises obtainingmeasures of first and second optical densities of said biological systembased on said first and second portions of detected light and fittingsaid measures of optical densities to said generally linear model. 7.The method of claim 2 wherein the step of comparing said first andsecond portions of the delivered light comprises determining a measureof the concentration of one or more of said solutes based on acomparison of said characterization of said biological system against apredetermined scale.
 8. The method of claim 1 further comprising thestep of determining a measure of a concentration of one or more of saidsolutes in said biological system based on a predetermined concentrationscale.
 9. The method of claim 1 wherein said steps of detecting saidfirst and second portions of said delivered light comprise measuringfirst and second intensities (I₁, I₂) corresponding to the intensitiesof said first and second portions of light, respectively.
 10. The methodof claim 9 further comprising the step of determining changes, overtime, in said first and second intensities (I₁, I₂) relative to firstand second reference intensities (I_(1,ref), I_(2,ref)).
 11. The methodof claim 10 wherein said step of determining relative changes in saidfirst and second intensities further comprises respectively determiningfirst and second optical densities (OD₁, OD₂):${OD}_{1} = {\log\quad\left( \frac{I_{1}}{I_{1,{ref}}} \right)}$${OD}_{2} = {\log\quad{\left( \frac{I_{2}}{I_{2,{ref}}} \right).}}$ 12.The method of claim 11 wherein said step of comparing said first andsecond portions of the delivered light comprises using a linear modelrelating said first and second optical densities to distances (ρ₁, ρ₂)representative of said first and second average path lengths to obtain acharacterization of said biological system representative of theconcentration of one or more of said solutes in said biological system.13. The method of claim 12 wherein the characterization that is obtainedis a slope (m) determined by$m = {\frac{{OD}_{2} - {OD}_{1}}{\rho_{2} - \rho_{1}}.}$
 14. The methodof claim 12 wherein the characterization that is obtained is anintercept (b) determined by$b = {\frac{{{OD}_{1} \cdot \rho_{2}} - {{OD}_{2} \cdot \rho_{1}}}{\rho_{2} - \rho_{1}}.}$15. The method of claim 1 further comprising the step of detecting athird portion of said delivered light, said third portion havingtraveled through said biological system along one or more pathscharacterized by a third average path length that is greater than saidfirst and second average path lengths.
 16. A system for monitoring asolute in a biological system comprising at least two sources of lighthaving a wavelength selected to be in a range wherein said solute issubstantially non-absorbing, a detector positioned at differentdistances with respect to said at least two detectors to detect at leastfirst and second portions of said delivered light, said first portionhaving traveled through said biological system along one or more pathscharacterized by a first average path length, and said second portionhaving traveled through said biological system along one or more pathscharacterized by a second average path length that is greater than saidfirst average path length, and a comparator adapted to compare saidfirst and second portions of the delivered light to monitorconcentration of said solute in said biological system.
 17. A method ofclaim 1, wherein said solute is a low molecular weight carbohydrate, analcohol, or an electrolyte.
 18. A method of claim 17, wherein saidsolute is mannitol, fructose, sucrose, glucose, propanediol, methanol,ethanol, sodium ion, potassium ion, or chloride ion.
 19. A method ofclaim 17, wherein said solute is sorbitol, magnesium ion, or calciumion.
 20. A method of claim 18, wherein said solute is glucose.
 21. Amethod of claim 18, wherein said solute is potassium.
 22. A method ofclaim 1, wherein said solute is bonded to a contrast agent.